bar01b.gif

For the Introduction / Rules / Schedule / Prizes / Position / Tutorial / etc. Please click here.

For all the Results, please click here. 

News
 

08 August, 00:22

The results are now published here.

08 August, 00:00

GONG! End of the tournament! Thank you all, it has been a great one as always. So many surprises and beautiful matrices, until the very end... Congratulations to Ralf and Arno for winning the 1st prize in several categories, and to all for a very high level of creativity. The results will be published in a few minutes.

07 August, 22:15

Ivan & Jan find a very nice B1/14/51!

07 August, 18:27

Arno had almost a B1/18/103! Which is a quite special one too. There are two solutions, which cannot of course be accepted for this tournament, nevertheless it could be viewed as correct according to the Codex! More info soon :)

07 August, 16:28

Ralf finds a splendid E2/6/28! Quite special.

07 August, 15:35

Well, words fail me... Arno found an unbelievable A1/19/122/2!!! Quite inimaginable just a few minutes ago. A very elaborate matrix, with several unique features that were not seen before in this tournament. The first one with 19 pieces to start with! Soon the end, thus you will have the chance of seeing it later today (tomorrow). Probably a winner for this category... unless someone comes up with better?! ;)

03 August, 15:04

He also finds two other nice entries: a D2/7/22 and a D2/8/25!

03 August, 11:05

Arno improves two records with a D2/5/14 and a D2/6/21!

01 August, 11:23

Ralf finds a very original D2/10/36! One week left, last finishing line :)

31 July, 11:23

Arno finds a very elegant D2/5/13!

30 July, 13:17

The calm before the storm... Ralf has found another gem with an incredible D1/18/67!!!

26 July, 10:34

Arno improves even more with a D1/18/62!

25 July, 18:19

Ralf finds two elegant entries: a B2/7/38 and a B2/8/42!

25 July, 15:05

Arno finds Ivan & Jan's very tricky E2/4/13!

25 July, 10:34

Wow... Arno continues to impress with an incredible D1/18/61!!! Well, I thought this month would also bring its lot of surprises... He also finds a B1/17/62!

24 July, 10:11

Arno starts the C2 category with two nice entries: a C2/9/36 and a C2/10/39!

23 July, 19:33

Ralf now takes the lead in the C1 category with an impressive C1/17/55/1!!! He also improves with a D1/14/44... Arno also improves with a beautiful D1/14/51!

23 July, 09:45

Well, we have a new D1 record! Arno finds a very elegant D1/16/49!!!

22 July, 13:50

Arno improves two records with a D2/9/30 and a D2/10/32!

21 July, 19:38

Arno finds a very nice D2/7/19!

21 July, 16:41

Which he improves with two nice entries: a D2/6/17 and a D2/7/18!

20 July, 09:23

Ralf follows with a second D2/7/17!

19 July, 22:33

And also an elegant D2/7/17!

19 July, 20:30

Cornel finds a second, very pretty D2/6/14!

16 July, 10:10

Arno finds a second D2/4/7, very different than the other one!

15 July, 17:38

Ralf is the first to greet the new domain, with two very nice entries: E2/9/56 and E2/10/59!

15 July, 15:38

Well, I wasn't that happy with my choice of domain name, too long... pfff... strange, I wanted ifaybish.com, but it was not available then (?!) so I chose that one. But then, I thought it might be possible to change, and indeed, it is not that hard. Except for a few dollars lost. O well... it is now officially: ifaybish.com :) The other one will also work for at least one year. So to celebrate this move to a new house, I added another puzzle, with an incredible solution...

14 July, 15:47

Given that the geocities site is closing, I had to set it up somewhere else. So I upgraded to a more professional webhosting, with the ability of redirecting automatically all files from geocities to that site (but unfortunately not to the correct subfolder). Thus some problems might occur in the coming days, if for example some DNS servers are not yet updated, or something else. It would be best if you update your bookmarks to the new pages.

13 July, 19:14

Ivan & Jan also find a very elegant E2/4/13! It is very close to Cornel's, I hesitated seeing it as different, but still it is somewhat different...

12 July, 19:42

Another unbelievable one from Ralf... should I say it with the risk of causing another shock?! Well, I have to inform you that Ralf found an amazing E1/17/87!!! Quite incredible it is, and a gem.

12 July, 12:42

Cornel continues to improve with an impressive E1/18/66!

10 July, 12:30

Well, they must be telepathic or something... Ralf just found a very elegant E2/5/23!!!

10 July, 11:08

Ivan & Jan find an incredible E2/5/22! Really original...

09 July, 22:57

And it is not over... He improves further with an E1/17/65!!!

09 July, 16:14

Cornel improves even more with an E1/16/63!

09 July, 12:05

Well, no one messes with Cornel... one takes his D1, he takes E1 back :) He found a most beautiful E1/17/63! Now half-way through the tournament, and so many gems have been discovered. And still half-way to go! I have no idea still how it might develop, there were surprises all the way, and surely not over... An interesting point is that most matrices are quite - if not very - different from one another, apart from the D2/4/7!

08 July, 16:22

Cornel already improves very nicely with an E1/13/52!

08 July, 15:24

I tried the matrix with the previous versions of Popeye: 4.47, 4.45 and 4.06, and they worked fine. Thus a problem only with the newest version. So maybe we should use the latest previous one, that is 4.47.

08 July, 14:46

Ivan & Jan take the lead in the D1 category with a very nice D1/15/43! They also improved an entry with an elegant B2/7/34... A slight worry, they uncovered a small bug in Popeye, which makes it not always show all the solutions for D/C kind of problems. To investigate a little bit, and to be more careful.

08 July, 11:04

Well... after a long period of silence, we have a new entry! :) Cornel finds a very nice E1/12/46! Many take their holidays during these months, which explains the low activity.

04 July, 16:59

I have created .pdf documents for each of the previous 4 tournaments. If you are interested, you can download them here: first, second, third, fourth  

04 July, 15:25

Very calm lately... time for another beautiful puzzle :)

02 July, 19:28

Hmm... how to say that, unbelievable sounds right?! Well, you will probably believe it, but will certainly be amazed, Ralf found an incredible B1/16/89!!! And with high style, a brilliant matrix... almost 100... in the B category! Who would have thought it is possible...

02 July, 11:55

Ivan & Jan respond with a very nice E1/13/58, taking the lead again!

02 July, 10:59

Cornel finds another beautiful one with an E2/6/26! Ralf also improves in the B2 category with two very nice entries: a B2/9/47 and a B2/10/52! This tournament is showing a very high degree of creativity, from all the composers. Many really special and elegant matrices have been found so far!

01 July, 10:25

Well, Ralf responds immediately, with a beautiful E1/15/58!!!

30 June, 10:22

Ivan & Ján and Ralf passed to high gears! Ivan & Ján found an amazing E1/13/57!!! And they also found an E2/7/40, E2/8/44, E2/9/49 and E2/10/52! Ralf also improved significantly with a beautiful and elegant E1/14/53!

29 June, 10:27

Well, he now found an E2/4/13!!! Quite an elegant one too, and not that easy to find...

28 June, 18:02

Cornel finds a third, very elegant E2/4/12!

28 June, 14:51

Ralf takes over E2 too with two nice entries: an E2/7/29 and an E2/8/31! (too many two's?! :))

28 June, 11:14

Cornel finds a nice E2/10/31!

27 June, 21:17

A little bit off topic, as I once "advertised" a beautiful documentary on the quantum / string theory (The Elegant Universe), if you are interested, there is another beautiful one on the 4th dimension in mathematics here. Highly recommended! :)

27 June, 21:00

Ralf takes the lead in the E1 category with a very nice E1/12/43!

27 June, 10:02

Cornel finds two more very elegant entries, an E2/4/12 and an E2/8/30!

26 June, 11:34

And Ralf follows with a very pretty E2/6/23... :)

25 June, 23:17

Cornel finds another gem! An E2/5/20!!!

25 June, 17:55

Arno finds an additional entry in B2, a B2/6/27!

25 June, 16:44

And Cornel already solved it!!! Impressively fast...

25 June, 15:04

New puzzle added! A nice one, with an elegant solution, as always :)

25 June, 13:49

Ivan & Ján continue the exploration of the E categories, with a gem of a matrix, an E2/4/12, and an elegant E1/15/42!

24 June, 19:33

And he also improves in the D1 category, and actually also takes the lead there with a very nice D1/16/40!

24 June, 17:15

Cornel improves with a C1/15/48/2!

24 June, 15:20

And for Arno, B2?! :) He finds another beauty, a B2/5/26!!!

24 June, 13:55

Well, for Ivan & Ján, it is E2! :) They found two nice entries: E2/5/15 and E2/7/26!

24 June, 11:13

Ralf definitely took over D2! He found a very nice series of entries: D2/8/24, D2/9/25 and D2/10/28!

23 June, 22:25

Ivan & Ján improve a B2 entry with an elegant B2/8/40!

23 June, 21:48

Ralf finds a nice D2/10/24! Almost a complete suite in D2...

23 June, 15:44

Arno finds a very elegant A2/6/30! A quite original idea...

23 June, 14:33

Welcome to Ján Golha! He and Ivan have teamed up and start with a beautiful E2/8/30!

23 June, 14:24

Ralf finds two nice entries: a D2/7/16 and a D2/8/21!

23 June, 10:22

And he even improves with a C1/16/48/2! Again he has set a high bar, but this time in the C1 category!

22 June, 12:42

Well, Cornel jumps to the high spheres with a very nice C1/15/47/2!!! Almost 50 in the C1 category is not often seen... and probably more is possible. Ralf finds two nice entries: a D2/5/12 and a D2/6/14!

21 June, 10:53

Action / Reaction... Cornel takes now the lead in the C1 category with a C1/15/38/3! :)

20 June, 21:52

Ralf takes the lead again in the D1 category with a D1/13/36!

20 June, 11:11

Well, when we all thought B2/4/12 might be the best... Arno comes up with a B2/4/13!!! And a very elegant one, as hard to find as can be (with just 4 pieces!)...

20 June, 10:22

Cornel improves with an A1/15/75/1!

19 June, 19:09

And Cornel already solved it! That was very fast...

19 June, 16:58

New puzzle added. Not an easy one, but most elegant for sure.

19 June, 12:08

To give a little more time to the participants, and as it was started a week after the start of the month, the deadline has been postponed also by a week, to the 7th of August at 23:59.

19 June, 11:59

Well, the tournament really seems to be kicking on... Cornel improves to... B1/16/75!!! And he also finds an A1/15/74/1! Amazing... but it is not over, Ralf, at 02:51 in the morning, finds a B1/16/69!!! Also a beauty, and a completely different matrix than Cornel's... That just shows there is still - a lot - yet to discover no doubt! Ivan also finds a very nice B2/7/33!

18 June, 20:09

Cornel also improves in the A1 cateogry with an A1/14/71/1!

18 June, 20:01

Wow... it is a surprise after surprise... Ralf finds a very elegant B2/9/46!!! The sky's the limit! :)

18 June, 18:09

Well... didn't take long, Cornel actually got to 70 with an incredible B1/15/71!!! That is quite an achievement... The bar is set very high now!

18 June, 12:54

Hold on your breadth... Cornel finds a beautiful B1/15/68!!! This is very impressive! He also finds an A1/14/68/1... Almost 70, who would have thought just a few days ago?!

18 June, 11:13

Cornel takes the lead again in the B1 category, with a B1/15/59! He also improves significantly in the A1 category with an A1/16/63/1... Ivan found another beautiful matrix, a B2/9/40! He also found a B2/10/41... Very few co-authors (just two!) in this tournament, it contrasts strongly with the previous ones. But of course, it is just the beginning...

17 June, 22:59

Ivan finds another gem of a matrix, a B2/8/35! So far there have been many very fine matrices, which conforts me in the fact that the condition is turning out to be quite prosperous in creative possibilities...

17 June, 15:56

Arno takes 1st place in the B1 category, with a very elegant B1/14/57! Cornel also improves nicely with an A1/12/55/1...

17 June, 09:34

Well, Juraj has done it again! He finds a really beautiful B2/5/20!!! I would qualify this one as very hard to find, despite the low dimension... Cornel continues to improve significantly, he finds a D1/16/36, an A2/10/44/1 and starts the A1 category with a very nice A1/11/52/1!

16 June, 22:45

He also starts in the B1 category with an interesting B1/13/40!

16 June, 15:03

Welcome to Ivan Skoba! He starts with a splendid E2/6/18!

16 June, 11:27

Well, Ralf and Cornel decided to battle it out in the C1 and D1 categories! Cornel takes the lead again!!! He finds a D1/15/35... and Ralf?! Well, he passes Cornel in the C1 with a C1/13/37/1...

15 June, 20:09

And Ralf takes the lead again! He finds a D1/12/33...

15 June, 19:46

Cornel takes 1st place with a D1/16/31!

15 June, 16:38

Ralf finds Cornel's D2/4/7!

15 June, 08:03

Cornel starts strongly with a C1/15/36/3! He also finds a D2/10/24, and thus completes a full suite...

14 June, 20:28

Is it possible to attain the 100 in the A category?! I really have the feeling that it just might be! But how, I have absolutely no idea, and probably some crazy matrix...

14 June, 20:00

Well, not that good a puzzle the 1st one. I thought in english it might be the same as in french, but it isn't. Thus it only works on natively french speaking persons, and probably of a certain generation... For all the rest, the solution is, well - obvious without hesitation - (I hope). So, a 2nd one, much better. With a most elegant solution, but like all good problems, not easy to find!

14 June, 13:52

Ralf finds a very nice D1/12/30!

14 June, 12:55

Cornel finds a nice series: D2/7/15, D2/8/17 and a D2/9/18! He is thus the first to enter the ranking for the number of records! And he also solves the first puzzle...

13 June, 14:55

Ralf starts in the D2 category with a nice D2/8/16! He also solves the first puzzle...

13 June, 12:47

Gilles also reaches 50 with a nice B1/15/50!

12 June, 19:56

And the second big surprise of the tournament... Ralf finds a beautiful B2/5/18!!! Really elegant, and far from evident. Thanks Ralf, easier for me now to keep track of the B2/5 :)

12 June, 19:26

Cornel aims for the 60... he finds a B1/14/56!

12 June, 15:55

Gilles is the first to solve it!

12 June, 14:41

To keep with old tradition, a new puzzle section is added. The first one is, well, quite interesting I found. I won't embarrass myself by saying that my very first thought when heard it was... well, wrong. Argh... did I say that out loud?!

12 June, 12:22

Cornel finds a nice A2/8/36/1 and a second B2/10/37!

11 June, 21:55

Cornel reaches 50 with B1/14/50!

11 June, 20:08

He also improves with a B1/13/48!

11 June, 16:22

Cornel starts the D category with a D2/4/7, D2/5/11 and D2/6/12!

11 June, 10:25

And Gilles finds it too! First co-authors for this tournament...

11 June, 00:03

A first great surprise, Juraj found a B2/4/12!!! Now that's a puzzle :)

10 June, 23:43

He also starts the E category with a very nice E2/4/11 and E2/5/13!

10 June, 22:15

Cornel finds a second B2/4/11!

10 June, 19:37

An additional important point. The legality of the initial positions will not be checked (except for the number of promoted pieces)! This is because the fairy conditions can create some very special structures, and it is not convenient to check for that. For example a white bishop on a1, and a pawn on b2 is legal in [Strict]Circe, but of course not in orthodox. And beside, one must have 32 pieces on board to have a chance of being a "legal" StrictCirce position!

10 June, 19:35

Many entries... Ralf starts the B1 category with a nice B1/14/45! Gilles is inspired, and finds a very elegant B2/5/17, a B2/9/37 and a B1/11/41! Arno also finds a B2/5/17 and a B2/9/33! Cornel gets to 1st place with a B1/16/46! Let the battle begin...

10 June, 16:41

Cornel improves with a B1/11/42!

10 June, 11:17

Welcome to Arno Tüngler! He starts - very - strongly with some very elegant entries: a B2/4/11 (!), B2/6/25 and a B2/7/29! The B2/4/11 will be a very nice puzzle to find for this tournament (if there are not even better)... Cornel also finds some nice entries: A2/8/41/1, and the first B1 entry: B1/13/42!

10 June, 01:13

Welcome to Juraj Lörinc! He starts with a nice B2/4/9. Gilles also finds a B2/4/9, and all three are quite different matrices!

9 June, 20:19

Welcome to Gilles Regniers! He starts nicely with a completely different B2/7/22! Cornel improves even more with a B2/5/17...

9 June, 16:44

Cornel improves with a nice B2/5/16!

9 June, 10:30

A few important questions came up, which need clarification and decision:

- Is it ok if a position is both Circe and StrictCirce? (Ralf, Arno)

At first I thought that it is ok. But thinking about it more, I realize that it is probably best not to be. For example it is possibe to find a B2/4/17 that satisfies both Circe and StrictCirce (found by both
Ralf and Arno), and it is probably possible for at least a few other entries to find such matrices (as Circe is a well-known condition, it may well be possible even to find several problems already existing). For higher dimensions I do not fear much. It would, I think, be very/extremely hard to find such ones that are both Circe and StrictCirce, and that are high records. Nevertheless, given the above, the answer will be no, defined as follow: If for a given position, both Circe and StrictCrice gives the same (same number of moves for the solutions) result, then it is not ok. Otherwise, it is!

- Are the kings included in the condition? (Ivan, Arno)

Well, first what does it mean? It means that if there is a piece on either e1 or e8, then either the white or the black king cannot be checked! Popeye by default does not include the kings, for this combination of conditions. Thus a king in check is always in check. But... indeed, being able to escape checks can be quite interesting, and the resulting positions very different! Thus the decision: A new category is added, E. This is only for positions without promoted pieces in the initial position. Instead of "Circe Immunchess", use: "Circe Immunchess
RexInclusiv". Also, to keep up with the logic, if it is the later, it cannot also be the former (or the former's former otherwise, "Circe" alone, can this actually happen?! hmm...)! With the same definition as above (the position is valid if the solutions given by the different conditions are different).

9 June, 10:29

Cornel continues to improve, and aims for a full suite, with a B2/7/22, and an A2/8/32/1!

8 June, 22:42

Cornel finds two new ones: A2/7/22/1 and A2/8/31/1!

8 June, 19:19

And he improves the B2/5 record with a B2/5/15!

8 June, 18:50

He also finds a B2/6/19...

8 June, 16:04

Cornel continues to improve with a B2/8/28!

8 June, 13:48

Welcome back Ralf Krätschmer! He starts with an elegant B2/5/13. A nice note is that this is quite different than Cornel's, and mine is also very different from those two! This means there will be a lot to explore. And - may I say probably - I believe there should be a quite better one for B2/5 (but I may be wrong, won't be a first).

8 June, 09:41

And we have our first entries! Welcome to Cornel Pacurar! He starts very nicely, with some neat matrices: B2/4/9, B2/5/13, B2/6/17 and an A2/6/18/1!

8 June, 00:06

As a technical comment, if you use Internet Explorer 8, this page does not show off very well. You have to go to compatibility mode by clicking on the "broken" button, next to the refresh one.

8 June, 00:00

GONG! Good luck to all! Hopefully the constraints have not scared you off... :) They will probably take some time to get used to.

7 June, 11:32

"!Dlrow olleh"


bar01b.gif

Rankings

Number of records entries in categories A2, B2, C2, D2 and E2 (minimum 10)
 

Competitor

Number of records

 Arno Tüngler

13

Ralf Krätschmer

10

 

 

 

 


Category A1
(best solution that can include promoted pieces in the initial position, minimum 50 moves)
 

Competitor

Number of moves

Number of pieces

Number of promoted pieces in the initial position

Date of sending

Arno Tüngler

122

19

2

07 August 2009, 15:19

Cornel Pacurar

75

15

1

19 June 2009, 20:30

 

 

 

 

 

 

 

 

 

 


Category B1 (best solution without a promoted piece in the initial position, minimum 40 moves)
 

Competitor

Number of moves

Number of pieces

Date of sending

Ralf Krätschmer

89

16

02 July 2009, 19:09

Cornel Pacurar

75

16

19 June 2009, 08:09

Arno Tüngler

62

17

24 July 2009, 22:34

Ivan Skoba & Ján Golha

51

14

07 August 2009, 21:51

Gilles Regniers

50

15

13 June 2009, 12:46

Ivan Skoba

41

10

18 June 2009, 07:46

 

 

 

 

 

 

 

 


Category C1 (best solution that can include promoted pieces in the initial position, minimum 35 moves)
 

Competitor

Number of moves

Number of pieces

Number of promoted pieces in the initial position

Date of sending

Ralf Krätschmer

55

17

1

23 July 2009, 15:26

Cornel Pacurar

48

15

2

24 June 2009, 17:13

 

 

 

 

 

 

 

 

 

 


Category D1
(best solution without a promoted piece in the initial position, minimum 30 moves)
 

Competitor

Number of moves

Number of pieces

Date of sending

Ralf Krätschmer

67

18

30 July 2009, 13:04

Arno Tüngler

62

18

26 July 2009, 08:05

Ivan Skoba & Ján Golha

43

15

07 July 2009, 12:59

Cornel Pacurar

40

16

24 June 2009, 19:27

 

 

 

 

 

Category A2 (initial position having at least one promoted piece, and better than equivalent category B2 ranking)
 

Number of pieces in total in the initial position

Competitors

Number of moves

Number of promoted pieces in the initial position

5

 

 

 

6

Arno Tüngler

30

1

7

 

 

 

8

 

 

 

9

 

 

 

10

 

 

 


Category B2 (initial position having no promoted pieces)
 

Number of pieces in total in the initial position

Competitors

Number of moves

4

Arno Tüngler

13

5

Arno Tüngler

26

6

Arno Tüngler

27

7

Ralf Krätschmer

38

8

Ralf Krätschmer

42

9

Ralf Krätschmer

47

10

Ralf Krätschmer

52


Category C2 (initial position having at least one promoted pieces, and better than equivalent category D2 ranking)
 

Number of pieces in total in the initial position

Competitors

Number of moves

Number of promoted pieces in the initial position

5

 

 

 

6

 

 

 

7

 

 

 

8

 

 

 

9

Arno Tüngler

36

1

10

Arno Tüngler

39

1


Category D2 (initial position having no promoted pieces)
 

Number of pieces in total in the initial position

Competitors

Number of moves

4

Cornel Pacurar, Ralf Krätschmer

Arno Tüngler

7

5

Arno Tüngler

14

6

Arno Tüngler

21

7

Arno Tüngler

22

8

Arno Tüngler

25

9

Arno Tüngler

30

10

Ralf Krätschmer

36


Rex-Inclusive

Category E1
(best solution without a promoted piece in the initial position, minimum 40 moves)
 

Competitor

Number of moves

Number of pieces

Date of sending

Ralf Krätschmer

87

17

12 July 2009, 19:19

Cornel Pacurar

66

18

12 July 2009, 04:09

Ivan Skoba & Ján Golha

58

13

02 July 2009, 11:47

 

 

 

 


Category E2 (initial position having no promoted piece)
 

Number of pieces in total in the initial position

Competitors

Number of moves

4

Cornel Pacurar

Ivan Skoba & Ján Golha, Arno Tüngler

13

5

Ralf Krätschmer

23

6

Ralf Krätschmer

28

7

Ivan Skoba & Ján Golha

40

8

Ivan Skoba & Ján Golha

44

9

Ralf Krätschmer

56

10

Ralf Krätschmer

59


Outside competition: Category Puzzle
 

Puzzle

Statement

Competitors

1

Only the first solution sent will be accepted, so think carefully!

The mother of Toto has three sons: Riri, Fifi, and ?

Source: Television Quiz (it tricked the person asked, and also the then champion!)
Original Source: Unknown
Comment: As explained in the text, it is not such a good puzzle, as it only "works" on french-speaking persons.

Gilles Regniers, Ralf Krätschmer, Cornel Pacurar

2

Let's imagine we are professional chess players, and we must plan our season's tournaments schedule.

We get a list of tournaments schedules (from xx/xx/xx to yy/yy/yy, without breaks) from the organizers for the entire season, at the beginning of it.

All the tournaments have exactly the same prizes, and are of the same strength. Geographical location is not taken in account.

We cannot play in two tournaments at the same time.

As professionals, we wish to earn the largest amount of money (ok, I see a debate here, let's just - assume - it is for now).

Thus we would like ideally to play in the most number of tournaments in the season.

What algorithm could we devise, in order to find that maximum? Assuming there are a lot of tournaments in a season.

Source: Algorithmics

 

3

Here is an absolute gem. It may seem quasi impossible at first, bordering on the insanely difficult, but... the solution is a beauty. And quite straightforward - once known -. That said, it is nevertheless difficult to find.

What is the 99th digit to the right of the decimal point in the decimal expansion of

Source: Mathematical Mind-Benders by Peter Winkler.
Original Source: The
Emissary newsletter, E. Berlekamp and J.P.Buhler, "Puzzle Column".

Cornel Pacurar

4

Given 15 dots in a line:

.   .   .   .   .   .   .   .   .   .   .   .   .   .   .

Two players take turns placing an X through one of the dots. The first player to mark off a dot so that (at least) three consecutive dots are marked is the winner.

Which player should win, the one who goes first, or the one who goes second?

Source: Problem Solving Through Recreational Mathematics by Bonnie Averbach and Orin Chein.

Cornel Pacurar

5

This one is from the book Gödel, Escher, Bach: an Eternal Golden Braid by Douglas R. Hofstadter.

A very interesting book, linking all of the three seemingly separate famous person's representations and concepts into a coherent framework.

In it he presents the following elegant problem, called the MIU puzzle as you will soon see why:

Given the Symbols: M, I, U

Starting with the Axiom: MI

With rules:
1. If xI is a theorem, so is xIU
2. If Mx is a theorem, so is Mxx
3. In any theorem, III can be replaced by U
4. UU can be dropped from any theorem

Question: Is it possible to end up with MU ?

Ok, this may sound somewhat abstract and nonsensical, but it is really quite straightforward.

Let's work out an example:

1. MI
2. MII (from rule 2)
3. MIIII (from rule 2)
4. MIIIIU (from rule 1)
5. MIIIIUIIIIU (from rule 2)
6. MIUUIUU (from rule 3)
7. MIIUU (from rule 4)

etc.

It is not at all clear at first sight that this either might, or might not be possible. Indeed, it could be that one must go to a theorem a thousand, or even much more, word long, and then all simplifies magically to MU.

Of course if I present it, there must something special and beautiful to the solution, and not overly difficult.

 

6

Given a rectangle of nxm (n and m >=2) squares.

Two persons play the following game: each one on turn removes a set of squares, starting at one of the square, and including all the squares that are above / right to it. The one who (must) take the low left unique square loses.

For example, suppose we play with a 2x2 initial square.

A starts and removes the upper right square.

B now has a problem, whichever square he takes, upper-left or down-right, A will take the other one, and win.

Question: Does the first to play always win, or it depends on the initial values of n and m?

Source: Mathematical Puzzles: A Connoisseur's Collection by Peter Winkler

 


bar01b.gif